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arXiv · 2307.01841

Traces and Time: a de Sitter Black Hole correspondence

Cesar Gomez
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Abstract

We describe how general covariance for QFT defined on a space-time background with horizons leads to the need of adding an extra quantum degree of freedom. The definition of traces and entropies involves the use of a formally thermal state (weight) on the algebra of observables of the added degree of freedom. This extra degree of freedom is promoted into a physical clock after defining an hermitian and positive clock Hamiltonian. The so modified weight can be used to associate to both dS and the BH a type $II_1$ factor and a finite trace. The Murray-von Neumann dimension ( coupling constant) for this type $II_1$ description of the black hole naturally produces an algebraic version of Page's curve.

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Cesar Gomez. 2023-07-04. Traces and Time: a de Sitter Black Hole correspondence. https://arxiv.org/abs/2307.01841

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